Georgian TV broadcast scuffles between ruling party and opposition lawmakers, who pushed each other and gesticulated angrily during debates on the bill, which government critics and Western countries have criticised as authoritarian and Russian-inspired.
If the bill passes on Tuesday, Georgian President Salome Zourabichvili has said she will veto it.
But parliament, which is controlled by the ruling party, can override her veto, setting the scene for further protests in a crisis that may determine whether Georgia stays on a path towards integration with Europe or pivots back towards Russia.
The bill would require organisations receiving more than 20 per cent of their funding from abroad to register as agents of foreign influence, imposing onerous disclosure requirements and punitive fines for violations.
Opponents have dubbed the bill "the Russian law", comparing it to Russian legislation used to target critics of Vladimir Putin's Kremlin.
Georgia's government says the bill is needed to promote transparency, combat "pseudo-liberal values" promoted by foreigners and preserve the country's sovereignty.
As Tuesday's debate got under way, about 1000 protesters picketed the fortress-like parliament building amid a major police presence, with water cannon idling nearby.
Demonstrations have been running for weeks and typically peak in the evening, where crowds numbering in the tens of thousands have mounted some of the biggest protests seen in Georgia since it regained independence from Moscow in 1991.
The European Union, which gave Georgia candidate status in December, has repeatedly said that the bill will be a barrier to Tbilisi's further integration with the bloc.
The ruling Georgian Dream party says it wants to join both the EU and NATO, even as it has adopted harsh anti-Western rhetoric in recent months.
Polls show Georgian public opinion is strongly supportive of EU integration, while many Georgians are hostile to Russia over Moscow's support for the breakaway regions of South Ossetia and Abkhazia.
The United States, Britain, Germany, Italy and France have all urged Georgia to withdraw the bill.
The Kremlin, which denies any role in inspiring the Georgian bill, said on Tuesday that the crisis was Tbilisi's internal affair and accused outside powers of meddling.
"We see an unveiled intervention in the internal affairs of Georgia from the outside," Kremlin spokesman Dmitry Peskov said.
"This is an internal matter of Georgia, we do not want to interfere there in any way."
